We've experienced the same issue after we migrated from Cognos 11.0.7 to 11.1.1, mostly during the first few days of the month.
Initially, we tried "nudging" the Batch Report Service as well, which only resolved the issue temporarily. After a few hours the reports started pending again. We involved IBM Support and they have suggested the following:
Have a separate Notification Store DB.
Increased the "Maximum number of processes for the batch report service during peak period".
Increase "Maximum memory for Websphere Liberty Profile in MB"
Additionally, we noticed the reports and jobs in pending state were triggered after one or more reports or jobs were running for a long time. Improving report run times helped. Also, several jobs were running reports concurrently. Those have been asked to run sequentially.
After about three months of tweaking and testing, we've not encountered the issue during the last two months. (knock on wood)
I hope this helps.